Multiple choice questions

Let a, b be constants. If the tangent line to the curve y = ar? + br at the point (1, 5) has slope 8, then a, b (respectively) are equal to (A) 3,2 (B) 3,1 (C) 4,2 (D) 5,1 (E) None of (A) - (D) Assume p > 0 is unit price and q > 0 is quantity. The Consumers' surplus for a demand function p = f(q) = 100 -2q and supply function p =g(q) = 20 + 3q is (A) 312 (B) 384 (C) 298 (D) 284 (E) 256 (F) None of (A) - (E) The value of re In( dr is VI (A) None of (B) - (F) (B) 4+2ve (C) 4e-2Ve (D) 4-2Ve (E) 4+3Ve (F) e A marginal-revenue function is given by " = ge" + q where q 2 0 is quantity and r(0) = 0. The value of r(1) is (A) 5/2 (B) 3 (C) 3/2 (D) 11/3 (E) None of (A) - (D) A number c E (3, 4) has the special property that "its square is 7 more than the number". If we apply Newton's method to the most appropriate quadratic function that has c as a root and take r1 = 3.5 as a first estimate of the number c, what would a2 be (rounded down to 3 decimal places) ? (A) 3.112 (B) 3.208 (C) 3.537 (D) 2.974 (E) A number not in (A) - (D) (F) We cannot answer the question because there is no appropriate quadratic function given. The maximum compound interest (expressed as a percentage of a principal, rounded down to one decimal place) that we can earn with 4% APR over 10 years is (A) 48.6 (B) 47.3 (C) 49.1 (D) 50.8 (E) A number not in (A) - (D) (F) We cannot answer the question because there is no principal or compounding frequency given. The area of the region that is enclosed between the curves r = y' and y = 1 - 2 is (A) 7/2 (B) 11/3 (C) 9/2 (D) 5 (E) 13/2 (F) None of (A) - (E)